[RPG] Does a Magic Staff count as a magic weapon

Some basic math, but first a rule

From compendium:

Staff (implement)

A staff is a shaft, usually of wood, that is typically as tall as or slightly taller than its wielder. Staffs are sometimes crowned with decorative crystals or other symbols of magical power. This implement also counts as a quarterstaff. Even a creature who doesn’t have proficiency with the staff as an implement can use it as a weapon, but if the staff is magical, the creature cannot use its properties or powers, only its enhancement bonus and critical hit effect.

Staffs (and other implements that are weapons) can apply their enhancement bonuses to regular weapon attacks made through the weapon (but powers and properties tend to be tied to implement attack powers.)

Thus you get the +2 to hit and +2 to damage on both implement attacks and weapon attacks made with the Magic Staff +2.

Math example: Implement attacks using your Int would be Int Mod + half level + enhancement bonus. Damage-wise its usually Mod Dam + feat + enhancement. Assuming you are level 6: 5+3+2+? = your bonus to hit. Assuming you have no feats (like expertise feats or damage focus feats) thats a +10 to hit and a +7 to damage.

No

DMG p.139:

A scepter or just a heavy cylinder, a magic rod is typically made of metal, wood, or bone. It's about 2 or 3 feet long, 1 inch thick, and 2 to 5 pounds.

A quarterstaff is about the same weight but 6 to 9 feet long i.e. more than twice as big.

Essentially, a rod is a "stick" - you could try to make a case that it is similar to a club but clubs generally have weighted ends, albeit not as weighted as a mace.